IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v47y2016i2d10.1007_s13226-016-0185-4.html
   My bibliography  Save this article

Generalising diagonal strict concavity property for uniqueness of Nash equilibrium

Author

Listed:
  • Eitan Altman

    (INRIA Sophia Antipolis
    LINCS)

  • Manjesh Kumar Hanawal

    (Indian Institute of Technology Bombay)

  • Rajesh Sundaresan

    (Indian Institute of Science)

Abstract

In this paper, we extend the notion of diagonally strictly concave functions and use it to provide a sufficient condition for uniqueness of Nash equilibrium in some concave games. We then provide an alternative proof of the existence and uniqueness of Nash equilibrium for a network resource allocation game arising from the so-called Kelly mechanism by verifying the new sufficient condition. We then establish that the equilibrium resulting from the differential pricing in the Kelly mechanism is related to a normalised Nash equilibrium of a game with coupled strategy space.

Suggested Citation

  • Eitan Altman & Manjesh Kumar Hanawal & Rajesh Sundaresan, 2016. "Generalising diagonal strict concavity property for uniqueness of Nash equilibrium," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(2), pages 213-228, June.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:2:d:10.1007_s13226-016-0185-4
    DOI: 10.1007/s13226-016-0185-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-016-0185-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-016-0185-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Oran Richman & Nahum Shimkin, 2007. "Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 215-232, February.
    2. Ramesh Johari & John N. Tsitsiklis, 2004. "Efficiency Loss in a Network Resource Allocation Game," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 407-435, August.
    3. Ramesh Johari & John N. Tsitsiklis, 2009. "Efficiency of Scalar-Parameterized Mechanisms," Operations Research, INFORMS, vol. 57(4), pages 823-839, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shiva Raj Pokhrel & Carey Williamson, 2022. "A Game-Theoretic Rent-Seeking Framework for Improving Multipath TCP Performance," Future Internet, MDPI, vol. 14(9), pages 1-23, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Frank Kelly & Peter Key & Neil Walton, 2016. "Efficient Advert Assignment," Operations Research, INFORMS, vol. 64(4), pages 822-837, August.
    2. Ramesh Johari & John N. Tsitsiklis, 2011. "Parameterized Supply Function Bidding: Equilibrium and Efficiency," Operations Research, INFORMS, vol. 59(5), pages 1079-1089, October.
    3. Xupeng Wei & Achilleas Anastasopoulos, 2021. "Mechanism Design for Demand Management in Energy Communities," Games, MDPI, vol. 12(3), pages 1-34, July.
    4. Ioannis Caragiannis & Alexandros A. Voudouris, 2021. "The Efficiency of Resource Allocation Mechanisms for Budget-Constrained Users," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 503-523, May.
    5. Thirumulanathan, D. & Vinay, H. & Bhashyam, Srikrishna & Sundaresan, Rajesh, 2017. "Almost budget balanced mechanisms with scalar bids for allocation of a divisible good," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1196-1207.
    6. Ashish R. Hota & Siddharth Garg & Shreyas Sundaram, 2014. "Fragility of the Commons under Prospect-Theoretic Risk Attitudes," Papers 1408.5951, arXiv.org, revised Jun 2016.
    7. Hota, Ashish R. & Garg, Siddharth & Sundaram, Shreyas, 2016. "Fragility of the commons under prospect-theoretic risk attitudes," Games and Economic Behavior, Elsevier, vol. 98(C), pages 135-164.
    8. Tobias Harks & Konstantin Miller, 2011. "The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games," Operations Research, INFORMS, vol. 59(6), pages 1491-1503, December.
    9. Sreekumaran, Harikrishnan & Hota, Ashish R. & Liu, Andrew L. & Uhan, Nelson A. & Sundaram, Shreyas, 2021. "Equilibrium strategies for multiple interdictors on a common network," European Journal of Operational Research, Elsevier, vol. 288(2), pages 523-538.
    10. Simai He & Jay Sethuraman & Xuan Wang & Jiawei Zhang, 2017. "A NonCooperative Approach to Cost Allocation in Joint Replenishment," Operations Research, INFORMS, vol. 65(6), pages 1562-1573, December.
    11. Meng Zhang & Deepanshu Vasal, 2020. "Mechanism Design for Large Scale Network Utility Maximization," Papers 2003.04263, arXiv.org, revised Jan 2021.
    12. Pálvölgyi, Dénes & Peters, Hans & Vermeulen, Dries, 2014. "A strategic approach to multiple estate division problems," Games and Economic Behavior, Elsevier, vol. 88(C), pages 135-152.
    13. Gur, Yonatan & Iancu, Dan & Warnes, Xavier, 2020. "Value Loss in Allocation Systems with Provider Guarantees," Research Papers 3813, Stanford University, Graduate School of Business.
    14. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
    15. Saurabh Amin & Patrick Jaillet & Haripriya Pulyassary & Manxi Wu, 2023. "Market Design for Dynamic Pricing and Pooling in Capacitated Networks," Papers 2307.03994, arXiv.org, revised Nov 2023.
    16. Simina Br^anzei, 2019. "Tit-for-Tat Dynamics and Market Volatility," Papers 1911.03629, arXiv.org, revised Jan 2024.
    17. Balmaceda, Felipe & Balseiro, Santiago R. & Correa, José R. & Stier-Moses, Nicolás E., 2016. "Bounds on the welfare loss from moral hazard with limited liability," Games and Economic Behavior, Elsevier, vol. 95(C), pages 137-155.
    18. Ragavendran Gopalakrishnan & Jason R. Marden & Adam Wierman, 2014. "Potential Games Are Necessary to Ensure Pure Nash Equilibria in Cost Sharing Games," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1252-1296, November.
    19. Rébillé, Yann & Richefort, Lionel, 2014. "Equilibrium existence and uniqueness in network games with additive preferences," European Journal of Operational Research, Elsevier, vol. 232(3), pages 601-606.
    20. Moulin, Hervé, 2010. "An efficient and almost budget balanced cost sharing method," Games and Economic Behavior, Elsevier, vol. 70(1), pages 107-131, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:indpam:v:47:y:2016:i:2:d:10.1007_s13226-016-0185-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.